Orthogonal 2002-01-04 23:56:03 2005-03-19 09:45:11 Definition \usepackage{amssymb} \usepackage{amsmath} \usepackage{amsfonts} \usepackage{graphicx} \usepackage{xypic} The word orthogonal comes from the Greek \emph{orthe} and \emph{gonia}, or ``right angle.'' It was originally used as synonym of perpendicular. This is where the use of ``orthogonal'' in orthogonal lines, orthogonal circles, and other geometric terms come from. In the realm of linear algebra, two vectors are orthogonal when their dot product is zero, which gave rise a generalization of two vectors on some inner product space (not necessarily dot product) being orthogonal when their inner product is zero. There are also particular definitions on the following entries: \begin{itemize} \item orthogonal matrices \item orthogonal polynomials \item orthogonal vectors \end{itemize} In a more broad sense, it can be said that two objects are orthogonal if they do not ``coincide'' in some way.